Numerical Investigation of the Effect of Heterogeneous Pore Structures on Elastic Properties of Tight Gas Sandstones

Strong heterogeneity of pore microstructures leads to complicated velocity-porosity relationships in tight sandstone that cannot be well explained by conventional empirical formulas. To better understand the effect of complex pore structures on elastic properties of tight gas sandstone, we compared three rock physics models. In the first model, we used a single aspect ratio value to quantify varied pore geometry in the tight sands. In the second model, complex pore space was equivalent to the combination of high-aspect-ratio round pores (stiff pores) and low-aspect-ratio compliant microcracks (soft pores). In the third multiple pore-aspect-ratio model, pore spaces are represented using a set of pores with varied values of aspect ratio following statistical normal distribution. Modeling results showed that complex velocity-porosity relationships could be interpreted by the variations in pore aspect ratio in the first model, by the fraction of soft pores in the second model, and by the mean value and variance in the third statistical model. For a given mean value in the third model, higher variance of the multiple pore-aspect-ratio indicated stronger heterogeneity of pore spaces. Further studies on rock physical inversion showed that, compared with the first single pore-aspect-ratio model, the second dual-pore model gave better prediction in shear wave velocity by regarding the soft pore fraction as a fitting parameter. This finding revealed that the dual-pore model could be a more realistic representation of tight sandstone. The third statistical model showed comparable precision in the prediction of shear wave velocity compared with the dual-pore model; however, uncertainty existed for simultaneously determining mean value and variance of pore aspect ratio. On the basis of the dual-pore model, we evaluated the elastic modulus of dry frames of the tight sandstone using logging data in a borehole. Compared with empirical formulas, such as the Krief methods, the method in this paper provided a more rigorous way to determine elastic properties of dry frames for the tight sandstone. Comparisons of rock physical modeling methods offer a better understanding of the microstructures controlling the elastic behaviors of tight gas sandstone.